Question

In an experiment with Foucault's apparatus, the various distances used are as follows :

Distance between the rotating and the fixed mirror = 16 m

Distance between the lens and the rotating mirror = 6 m,

Distance between thesource and the lens = 2 m.

When the mirror is rotated at a speed of 356 revolutions per seconod, the image shifts by 0.7 mm. Calculate the speed of light from these data.

Answer 1

In the given Foucault experiment,
R = distance between fixed and rotating mirror = 16 m
w = Angular speed = 356 rev/s
= $356\times 2\pi$ rad/sec
b = distance between lens and rotating mirror = 6 m
a = Distance between source and lens
2 m
s =shift in image = 0.7 m = 0.7 $\times {10}^3$ m
So, speed of light is given by

c= 4 $R^2\frac{wa}{s(R+b)}$

= $\frac{4\times (16{)}^2\times 356\times 2\pi \times 2}{\left(0.7\right)\times {10}^{-3}(16+6)}$

= $2.975\times {10}^8$ m/s